They were spotted together at a Miami cafe a day after both Musk and Heard confirmed their relationship was over.

The two arrived together in a black Tesla and seemed friendly with each other.

As Musk visited the Aquaman set and prepared to fly out last night, he and Heard told the Gold Coast Bulletin; "Having read recent articles about our relationship, we would like to speak for ourselves.

"The distance has been really tough on our relationship, because we haven't been able to see each other much. All relationships have their ups and downs, of course.

"People occasionally send out speculation, which has no basis in fact, without our knowledge, believing that they have our best interests in mind. Sometimes, other agendas are at work. It can get a little weird ...

"However, we would like to state directly that we have the utmost respect for one another, and it would be troubling if anyone had the impression that we thought otherwise.

"As a closing note, it is worth bearing in mind that events are always amplified and dramatised in a high-profile relationship, whether the people involved like it or not (and we definitely don't). The reality is that this is just a normal relationship with a giant magnifying glass applied."

Amber Heard with Gold Coast Bulletin journalist Sally Coates at Paddock Bakery, Miami. The pair would not take a photo with them both in it, but were happy to pose separately. Picture taken by Elon Musk.

The couple announced their split last weekend, revealing the distance between them was a factor.

Heard has been on the Gold Coast filming Aquaman while Musk is predominantly in the US busy with the unveiling of the latest Tesla car and the coming launch of Space X's Falcon Heavy rocket.

A source close to the couple said Musk was believed to be dismayed the slur came from within his own company.

"He's running two huge companies," they said.

"He's got a lot of people acting on his behalf.

"It may be that they're trying to be protective, but they're just mistaken."